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摘要
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Visual cryptography encrypts the secret image into n
shares (transparency) so that only stacking a qualified number of shares can recover the secret image by the human visual system while no information can be revealed without a large enough number of shares. This paper investigates the (k,n)
-threshold Visual Secret Sharing (VSS) model, where one can decrypt the original image by stacking at least k shares and get nothing with less than
shares. There are two main approaches, which have been showed equivalent in some sense, in the literature: codebook-based schemes and random-grid-based schemes; the former is the case of this paper. In general, given any positive integers k
and n, it is not easy to design a valid scheme for the
(k,n)-threshold VSS model. In this paper, we propose a simple strategy to construct an efficient scheme for the (k,n)-threshold VSS model for any positive integers 2≦k≦n. The crucial idea is to establish a seemingly unrelated connection between the (k,n)-threshold VSS scheme and a mathematical structure — the generalized Pascal’s triangle. This paper improves and extends previous results in four aspects:
• Our construction offers a unified viewpoint and covers several known results.
• The resulting scheme has a progressive-viewing property that means the more shares being stacked together the clearer the secret image would be revealed.
• The proposed scheme can be constructed explicitly and efficiently based on the generalized Pascal’s triangle without a computer.
• Performance of the proposed scheme is comparable with known results. |